Let f(x) = ∫₀^x (t + sin(1 - e^t)) dt, x ∈ ℝ. Find lim_(x → 0) f(… | JEE Main 2024 Mathematics PYQ | Jeeify

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MCQMediumJEE Main 2024 · 4 April, Shift 2Limits

Let $f(x)$ = $\int_0^x \left(t + \sin(1 - e^t)\right) \, dt$ , $x \in \mathbb{R}$ . Find $\lim_{x \to 0} \frac{f(x)}{x^3}$ :

A
$\frac{1}{6}$
B
$-\frac{1}{6}$
C
$-\frac{2}{3}$
D
$\frac{2}{3}$

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